We report comprehensive 77 Se NMR measurements on a single crystalline sample of the recently discovered FeSe-based high-temperature superconductor K x Fe 2 - y Se 2 ( T c = 33 K) in a broad temperature range up to 290 K. Despite deviations from the stoichiometric KFe 2 Se 2 composition, we observed 77 Se NMR line shapes as narrow as 4.5 kHz under a magnetic field applied along the crystal c axis, and found no evidence for co-existence of magnetic order with superconductivity. On the other hand, the 77 Se NMR line shape splits into two peaks withmore » equal intensities at all temperatures when we apply the magnetic field along the ab plane. This suggests that K vacancies may have a superstructure and that the local symmetry of the Se sites is lower than the tetragonal fourfold symmetry of the average structure. This effect might be a prerequisite for stabilizing the s ± symmetry of superconductivity in the absence of the hole bands at the Brillouin zone center. From the increase of NMR linewidth below T c induced by the Abrikosov lattice of superconducting vortices, we estimate the in-plane penetration depth λ ab ~ 290 nm and the carrier concentration n e ~ 1 × 10 + 21 cm - 3 . Our Knight shift 77 K data indicate that the uniform spin susceptibility decreases progressively with temperature, in analogy with the case of FeSe ( T c ~ 9 K) as well as other FeAs high- T c systems. The strong suppression of 77 K observed immediately below T c for all crystal orientations is consistent with a singlet pairing of Cooper pairs. We do not however observe the Hebel-Slichter coherence peak of the nuclear spin-lattice relaxation rate 1 / T 1 immediately below T c , expected for conventional BCS s-wave superconductors. In contrast with the case of FeSe, we do not observe evidence for an enhancement of low-frequency antiferromagnetic spin fluctuations near T c in 1 / T 1 T . Instead, 1 / T 1 T exhibits qualitatively the same behavior as overdoped non-superconducting Ba(Fe 1 - x Co x ) 2 As 2 with x ~ 0 . 14 or greater, where hole bands are missing in the Brillouin zone center. We will discuss the implications of our results on the unknown mechanism of high-temperature superconductivity in FeSe and FeAs systems.« less